標題: Extracting Computational Entropy and Learning Noisy Linear Functions
作者: Lee, Chia-Jung
Lu, Chi-Jen
Tsai, Shi-Chun
資訊工程學系
Department of Computer Science
公開日期: 2009
摘要: We study the task of deterministically extracting randomness from sources containing computational entropy. The sources we consider have the form of a conditional distribution (f(X)vertical bar X), for some function f and some distribution X, and we say that such a source has computational min-entropy k if any circuit of size 2(k) can only predict f(x) correctly with probability at most 2(-k) given input x sampled from X. We first show that it is impossible to have a seedless extractor to extract from one single source of this kind. Then we show that it becomes possible if we are allowed a seed which is weakly random (instead of perfectly random) but contains some statistical min-entropy, or even a seed which is not random at all but contains some computational min-entropy. This can be seen as a step toward extending the study of multi-source extractors from the traditional, statistical setting to a computational setting. We reduce the task of constructing such extractors to a problem in learning theory: learning linear functions under arbitrary distribution with adversarial noise. For this problem, we provide a learning algorithm, which may have interest of its own.
URI: http://hdl.handle.net/11536/15840
ISBN: 978-3-642-02881-6
ISSN: 0302-9743
期刊: COMPUTING AND COMBINATORICS, PROCEEDINGS
Volume: 5609
起始頁: 338
結束頁: 347
顯示於類別:會議論文